{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "ae1512d8",
   "metadata": {},
   "source": [
    "# Analyzing a Brain Dynamics Model\n",
    "\n",
    "[![Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/brainpy/brainpy/blob/master/docs_version2/quickstart/analysis.ipynb)\n",
    "[![Open in Kaggle](https://kaggle.com/static/images/open-in-kaggle.svg)](https://kaggle.com/kernels/welcome?src=https://github.com/brainpy/brainpy/blob/master/docs_version2/quickstart/analysis.ipynb)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c83bdd21",
   "metadata": {},
   "source": [
    "@[Xiaoyu Chen](mailto:c-xy17@tsinghua.org.cn) @[Chaoming Wang](https://github.com/chaoming0625)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "072ee7b8",
   "metadata": {},
   "source": [
    "In BrainPy, defined models can not only be used for simulation, but also be capable of performing automatic dynamics analysis.\n",
    "\n",
    "BrainPy provides rich interfaces to support analysis, including\n",
    "\n",
    "- Phase plane analysis, bifurcation analysis, and fast-slow bifurcation analysis for [low-dimensional systems](../tutorial_analysis/lowdim_analysis.ipynb);\n",
    "- linearization analysis and fixed/slow point finding for [high-dimensional systems](../tutorial_analysis/highdim_analysis.ipynb). \n",
    "\n",
    "Here we will introduce three brief examples of 1-D bifurcation analysis and 2-D phase plane analysis. For more detailsand more examples, please refer to the tutorials of [dynamics analysis](../tutorial_analysis/index.rst)."
   ]
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-06T03:11:09.138132Z",
     "start_time": "2025-10-06T03:11:05.084625Z"
    }
   },
   "cell_type": "code",
   "source": [
    "import brainpy as bp\n",
    "import brainpy.math as bm\n",
    "\n",
    "bm.set_platform('cpu')\n",
    "\n",
    "bm.enable_x64()  # it's better to use x64 computation"
   ],
   "id": "f189edde76fd1be3",
   "outputs": [],
   "execution_count": 1
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-06T03:11:09.149334Z",
     "start_time": "2025-10-06T03:11:09.143958Z"
    }
   },
   "cell_type": "code",
   "source": "bp.__version__",
   "id": "94cbc061644eb609",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'3.0.0'"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 2
  },
  {
   "cell_type": "markdown",
   "id": "f418d87b",
   "metadata": {},
   "source": [
    "## Bifurcation analysis of a 1D model"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b600c817",
   "metadata": {},
   "source": [
    "Here, we demonstrate how to perform a bifurcation analysis through a one-dimensional neuron model."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1ecf04d3eaf72477",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "Let's try to analyze how the external input influences the dynamics of the Exponential Integrate-and-Fire (ExpIF) model. The ExpIF model is a one-variable neuron model whose dynamics is defined by:\n",
    "\n",
    "$$\n",
    "\\tau {\\dot {V}}= - (V - V_\\mathrm{rest}) + \\Delta_T \\exp(\\frac{V - V_T}{\\Delta_T}) + RI \\\\\n",
    "\\mathrm{if}\\, \\, V > \\theta, \\quad  V \\gets  V_\\mathrm{reset}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9a46f462",
   "metadata": {},
   "source": [
    "We can analyze the change of ${\\dot {V}}$ with respect to $V$. First, let's generate an ExpIF model using pre-defined modules in ``brainpy.dyn``:"
   ]
  },
  {
   "cell_type": "code",
   "id": "8d6b11cb",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-06T03:11:09.192318Z",
     "start_time": "2025-10-06T03:11:09.153343Z"
    }
   },
   "source": [
    "expif = bp.dyn.ExpIF(1, delta_T=1.)"
   ],
   "outputs": [],
   "execution_count": 3
  },
  {
   "cell_type": "markdown",
   "id": "a818b78c",
   "metadata": {},
   "source": [
    "The default value of other parameters can be accessed directly by their names:"
   ]
  },
  {
   "cell_type": "code",
   "id": "040b7004",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-06T03:11:09.200445Z",
     "start_time": "2025-10-06T03:11:09.196324Z"
    }
   },
   "source": [
    "expif.V_rest, expif.V_T, expif.R, expif.tau"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-65.0, -59.9, 1.0, 10.0)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 4
  },
  {
   "cell_type": "markdown",
   "id": "09f5722a",
   "metadata": {},
   "source": [
    "After defining the model, we can use it for bifurcation analysis. Note that, the following analysis"
   ]
  },
  {
   "cell_type": "code",
   "id": "358060fb",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-06T03:11:11.126244Z",
     "start_time": "2025-10-06T03:11:09.205491Z"
    }
   },
   "source": [
    "bif = bp.analysis.Bifurcation1D(\n",
    "    model=expif,\n",
    "    target_vars={'V': [-70., -55.]},\n",
    "    target_pars={'I': [0., 6.]},\n",
    "    resolutions={'I': 0.01}\n",
    ")\n",
    "bif.plot_bifurcation(show=True)"
   ],
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "I am making bifurcation analysis ...\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    }
   ],
   "execution_count": 5
  },
  {
   "cell_type": "markdown",
   "id": "4f03e723",
   "metadata": {},
   "source": [
    "In the ``Bifurcation1D`` analyzer, ``model`` refers to the model to be analyzed (essentially the analyzer will access the derivative function in the model), ``target_vars`` denotes the target variables, ``target_pars`` denotes the changing parameters, and ``resolution`` determines  the resolution of the analysis."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a61faa7b",
   "metadata": {},
   "source": [
    "In the image above, there are two lines that \"merge\" together to form a bifurcation. The dots making up the lines refer to the fixed points of $\\mathrm{d}V/\\mathrm{d}t$. On the left of the bifurcation point (where two lines merge together), there are two fixed points where $\\mathrm{d}V/\\mathrm{d}t = 0$ given each external input $I_\\mathrm{ext}$. One of them is a stable point, and the other is an unstable one. When $I_\\mathrm{ext}$ increases, the two fixed points move closer to each other, overlap, and finally disappear.\n",
    "\n",
    "Bifurcation analysis provides insights for the dynamics of the model, for it indicates the number and the change of stable states with respect to different parameters."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "96ce2043",
   "metadata": {},
   "source": [
    "## Phase plane analysis of a 2D model"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6ab49f7e",
   "metadata": {},
   "source": [
    "Besides bifurcationi analysis, another important tool is phase plane analysis, which displays the trajectory of the variable point in the vector field. Let's take the [FitzHugh–Nagumo (FHN) neuron model](https://brainmodels.readthedocs.io/en/latest/apis/generated/brainmodels.neurons.FHN.html) as an example. The dynamics of the FHN model is given by:\n",
    "\n",
    "$$\n",
    "{\\dot {v}}=v-{\\frac {v^{3}}{3}}-w+I, \\\\\n",
    "\\tau {\\dot {w}}=v+a-bw.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0a3a0e53",
   "metadata": {},
   "source": [
    "Users can easily define a FHN model which is also provided by BrainPy:"
   ]
  },
  {
   "cell_type": "code",
   "id": "e6b176c7",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-06T03:11:13.155224Z",
     "start_time": "2025-10-06T03:11:13.150708Z"
    }
   },
   "source": [
    "fhn = bp.neurons.FHN(1)"
   ],
   "outputs": [],
   "execution_count": 6
  },
  {
   "cell_type": "markdown",
   "id": "b13e4ee9",
   "metadata": {},
   "source": [
    "Because there are two variables, $v$ and $w$, in the FHN model, we shall use 2-D phase plane analysis to visualize how these two variables change over time."
   ]
  },
  {
   "cell_type": "code",
   "id": "78078951",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-06T03:11:18.172452Z",
     "start_time": "2025-10-06T03:11:13.159524Z"
    }
   },
   "source": [
    "analyzer = bp.analysis.PhasePlane2D(\n",
    "  model=fhn,\n",
    "  target_vars={'V': [-3, 3], 'w': [-3., 3.]},\n",
    "  pars_update={'I_ext': 0.8}, \n",
    "  resolutions=0.01,\n",
    ")\n",
    "analyzer.plot_nullcline()\n",
    "analyzer.plot_vector_field()\n",
    "analyzer.plot_fixed_point()\n",
    "analyzer.plot_trajectory({'V': [-2.8], 'w': [-1.8]}, duration=100.)\n",
    "analyzer.show_figure()"
   ],
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "I am computing fx-nullcline ...\n",
      "I am evaluating fx-nullcline by optimization ...\n",
      "I am computing fy-nullcline ...\n",
      "I am evaluating fy-nullcline by optimization ...\n",
      "I am creating the vector field ...\n",
      "I am searching fixed points ...\n",
      "I am trying to find fixed points by optimization ...\n",
      "\tThere are 866 candidates\n",
      "I am trying to filter out duplicate fixed points ...\n",
      "\tFound 1 fixed points.\n",
      "\t#1 V=-0.2729223248467867, w=0.5338542697669653 is a unstable node.\n",
      "I am plotting the trajectory ...\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    }
   ],
   "execution_count": 7
  },
  {
   "cell_type": "markdown",
   "id": "247760da",
   "metadata": {},
   "source": [
    "In the ``PhasePlane2D`` analyzer, the parameters ``model``, ``target_vars``, and ``resolution`` is the same as those in ``Bifurcation1D``. ``pars_update`` specifies  the parameters to be updated during analysis. After defining the analyzer, users can visualize the nullcline, vector field, fixed points and the trajectory in the image. The phase plane gives users intuitive interpretation of the changes of $v$ and $w$ guided by the vector field (violet arrows)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f8c9850a60c8a2b0",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "## Slow point analysis of a high-dimensional system"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a42b23306515127c",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "BrainPy is also capable of performing fixed/slow point analysis of high-dimensional systems. Moreover, it can perform automatic linearization analysis around the fixed point.\n",
    "\n",
    "In the following, we use a gap junction coupled FitzHugh–Nagumo (FHN) network as an example to demonstrate how to find fixed/slow points of a high-dimensional system."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "24471089c2a5247d",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "We first define the gap junction coupled FHN network as the normal ``DynamicalSystem`` class."
   ]
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-06T03:11:18.191909Z",
     "start_time": "2025-10-06T03:11:18.186991Z"
    }
   },
   "cell_type": "code",
   "source": [
    "class GJCoupledFHN(bp.DynamicalSystem):\n",
    "  def __init__(self, num=4, method='exp_auto'):\n",
    "    super(GJCoupledFHN, self).__init__()\n",
    "\n",
    "    # parameters\n",
    "    self.num = num\n",
    "    self.a = 0.7\n",
    "    self.b = 0.8\n",
    "    self.tau = 12.5\n",
    "    self.gjw = 0.0001\n",
    "\n",
    "    # variables\n",
    "    self.V = bm.Variable(bm.random.uniform(-2, 2, num))\n",
    "    self.w = bm.Variable(bm.random.uniform(-2, 2, num))\n",
    "    self.Iext = bm.Variable(bm.zeros(num))\n",
    "\n",
    "    # functions\n",
    "    self.int_V = bp.odeint(self.dV, method=method)\n",
    "    self.int_w = bp.odeint(self.dw, method=method)\n",
    "\n",
    "  def dV(self, V, t, w, Iext=0.):\n",
    "    gj = (V.reshape((-1, 1)) - V).sum(axis=0) * self.gjw\n",
    "    dV = V - V * V * V / 3 - w + Iext + gj\n",
    "    return dV\n",
    "\n",
    "  def dw(self, w, t, V):\n",
    "    dw = (V + self.a - self.b * w) / self.tau\n",
    "    return dw\n",
    "\n",
    "  def update(self):\n",
    "    t = bp.share['t']\n",
    "    dt = bp.share['dt']\n",
    "    self.V.value = self.int_V(self.V, t, self.w, self.Iext, dt)\n",
    "    self.w.value = self.int_w(self.w, t, self.V, dt)\n",
    "    self.Iext[:] = 0."
   ],
   "id": "62c06826ea881085",
   "outputs": [],
   "execution_count": 8
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "Through simulation, we can easily find that this system has a limit cycle attractor, implying that an unstable fixed point exists.",
   "id": "bd289c5babf56803"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-10-06T03:11:18.834069Z",
     "start_time": "2025-10-06T03:11:18.197434Z"
    }
   },
   "cell_type": "code",
   "source": [
    "# initialize a network\n",
    "model = GJCoupledFHN(4)\n",
    "model.gjw = 0.1\n",
    "\n",
    "# simulation with an input\n",
    "Iext = bm.asarray([0., 0., 0., 0.6])\n",
    "runner = bp.DSRunner(model, monitors=['V'], inputs=['Iext', Iext])\n",
    "runner.run(300.)\n",
    "\n",
    "# visualization\n",
    "bp.visualize.line_plot(runner.mon.ts, runner.mon.V, legend='V',\n",
    "                       plot_ids=list(range(model.num)),\n",
    "                       show=True)"
   ],
   "id": "ef00bac56a9ad6a2",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "  0%|          | 0/3000 [00:00<?, ?it/s]"
      ],
      "application/vnd.jupyter.widget-view+json": {
       "version_major": 2,
       "version_minor": 0,
       "model_id": "876dfc0ecd9d4d9faf792c41adfe53bb"
      }
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "data": {
      "text/plain": [
       "<module 'matplotlib.pyplot' from 'C:\\\\Users\\\\adadu\\\\miniconda3\\\\envs\\\\bdp\\\\Lib\\\\site-packages\\\\matplotlib\\\\pyplot.py'>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 9
  },
  {
   "cell_type": "markdown",
   "id": "22084ff723d5331",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "Let's try to optimize the fixed points for this system. Note that we only take care of the variables ``V`` and ``w``. Different from the low-dimensional analyzer, we should provide the candidate fixed points or initial fixed points when using the high-dimensional analyzer."
   ]
  },
  {
   "cell_type": "code",
   "id": "90ce07cf2a0a8e3c",
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2025-10-06T03:11:28.618340Z",
     "start_time": "2025-10-06T03:11:18.841081Z"
    }
   },
   "source": [
    "# init a slow point finder\n",
    "finder = bp.analysis.SlowPointFinder(f_cell=model,\n",
    "                                     target_vars={'V': model.V, 'w': model.w},\n",
    "                                     inputs=[model.Iext, Iext])\n",
    "\n",
    "# optimize to find fixed points\n",
    "finder.find_fps_with_gd_method(\n",
    "  candidates={'V': bm.random.normal(0., 2., (1000, model.num)),\n",
    "              'w': bm.random.normal(0., 2., (1000, model.num))},\n",
    "  tolerance=1e-6,\n",
    "  num_batch=200,\n",
    "  optimizer=bp.optim.Adam(lr=bp.optim.ExponentialDecay(0.05, 1, 0.9999)),\n",
    ")\n",
    "\n",
    "# filter fixed points whose loss is bigger than the threshold\n",
    "finder.filter_loss(1e-8)\n",
    "\n",
    "# remove the duplicate fixed points\n",
    "finder.keep_unique()"
   ],
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "D:\\codes\\projects\\BrainPy\\brainpy\\version2\\optim\\scheduler.py:355: UserWarning: ExponentialDecay is abandoned, please use ExponentialDecayLR insteadly.\n",
      "  warnings.warn(\"ExponentialDecay is abandoned, please use ExponentialDecayLR insteadly.\")\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimizing with Adam(lr=ExponentialDecay(0.05, decay_steps=1, decay_rate=0.9999), last_call=-1), beta1=0.9, beta2=0.999, eps=1e-08) to find fixed points:\n",
      "    Batches 1-200 in 0.21 sec, Training loss 0.0003090011\n",
      "    Batches 201-400 in 0.17 sec, Training loss 0.0002248715\n",
      "    Batches 401-600 in 0.16 sec, Training loss 0.0001743008\n",
      "    Batches 601-800 in 0.17 sec, Training loss 0.0001384070\n",
      "    Batches 801-1000 in 0.17 sec, Training loss 0.0001113474\n",
      "    Batches 1001-1200 in 0.15 sec, Training loss 0.0000904299\n",
      "    Batches 1201-1400 in 0.16 sec, Training loss 0.0000740472\n",
      "    Batches 1401-1600 in 0.16 sec, Training loss 0.0000611285\n",
      "    Batches 1601-1800 in 0.14 sec, Training loss 0.0000508670\n",
      "    Batches 1801-2000 in 0.15 sec, Training loss 0.0000425829\n",
      "    Batches 2001-2200 in 0.17 sec, Training loss 0.0000358431\n",
      "    Batches 2201-2400 in 0.14 sec, Training loss 0.0000303130\n",
      "    Batches 2401-2600 in 0.17 sec, Training loss 0.0000257813\n",
      "    Batches 2601-2800 in 0.16 sec, Training loss 0.0000220679\n",
      "    Batches 2801-3000 in 0.17 sec, Training loss 0.0000190129\n",
      "    Batches 3001-3200 in 0.16 sec, Training loss 0.0000164848\n",
      "    Batches 3201-3400 in 0.16 sec, Training loss 0.0000143577\n",
      "    Batches 3401-3600 in 0.21 sec, Training loss 0.0000125881\n",
      "    Batches 3601-3800 in 0.18 sec, Training loss 0.0000111072\n",
      "    Batches 3801-4000 in 0.16 sec, Training loss 0.0000098631\n",
      "    Batches 4001-4200 in 0.17 sec, Training loss 0.0000088056\n",
      "    Batches 4201-4400 in 0.18 sec, Training loss 0.0000078957\n",
      "    Batches 4401-4600 in 0.15 sec, Training loss 0.0000071023\n",
      "    Batches 4601-4800 in 0.16 sec, Training loss 0.0000064047\n",
      "    Batches 4801-5000 in 0.15 sec, Training loss 0.0000057897\n",
      "    Batches 5001-5200 in 0.17 sec, Training loss 0.0000052540\n",
      "    Batches 5201-5400 in 0.18 sec, Training loss 0.0000047848\n",
      "    Batches 5401-5600 in 0.17 sec, Training loss 0.0000043685\n",
      "    Batches 5601-5800 in 0.19 sec, Training loss 0.0000039942\n",
      "    Batches 5801-6000 in 0.19 sec, Training loss 0.0000036524\n",
      "    Batches 6001-6200 in 0.17 sec, Training loss 0.0000033357\n",
      "    Batches 6201-6400 in 0.19 sec, Training loss 0.0000030365\n",
      "    Batches 6401-6600 in 0.17 sec, Training loss 0.0000027516\n",
      "    Batches 6601-6800 in 0.17 sec, Training loss 0.0000024813\n",
      "    Batches 6801-7000 in 0.18 sec, Training loss 0.0000022267\n",
      "    Batches 7001-7200 in 0.19 sec, Training loss 0.0000019877\n",
      "    Batches 7201-7400 in 0.17 sec, Training loss 0.0000017673\n",
      "    Batches 7401-7600 in 0.18 sec, Training loss 0.0000015686\n",
      "    Batches 7601-7800 in 0.16 sec, Training loss 0.0000013878\n",
      "    Batches 7801-8000 in 0.15 sec, Training loss 0.0000012206\n",
      "    Batches 8001-8200 in 0.16 sec, Training loss 0.0000010660\n",
      "    Batches 8201-8400 in 0.17 sec, Training loss 0.0000009238\n",
      "    Stop optimization as mean training loss 0.0000009238 is below tolerance 0.0000010000.\n",
      "Excluding fixed points with squared speed above tolerance 1e-08:\n",
      "    Kept 806/1000 fixed points with tolerance under 1e-08.\n",
      "Excluding non-unique fixed points:\n",
      "    Kept 1/806 unique fixed points with uniqueness tolerance 0.025.\n"
     ]
    }
   ],
   "execution_count": 10
  },
  {
   "cell_type": "code",
   "id": "45b81a4cdac07efa",
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2025-10-06T03:11:28.658260Z",
     "start_time": "2025-10-06T03:11:28.652386Z"
    }
   },
   "source": [
    "print('fixed points:', )\n",
    "finder.fixed_points"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "fixed points:\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "{'V': array([[-1.17757851, -1.17757846, -1.17757851, -0.81465051]]),\n",
       " 'w': array([[-0.59697314, -0.59697318, -0.59697314, -0.14331315]])}"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 11
  },
  {
   "cell_type": "code",
   "id": "adc5767da75ea8b2",
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2025-10-06T03:11:28.672866Z",
     "start_time": "2025-10-06T03:11:28.667084Z"
    }
   },
   "source": [
    "print('fixed point losses:', )\n",
    "finder.losses"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "fixed point losses:\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([1.00655151e-19])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 12
  },
  {
   "cell_type": "markdown",
   "id": "511b2ac23cb0c586",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "Let's perform the linearization analysis of the found fixed points, and visualize its decomposition results."
   ]
  },
  {
   "cell_type": "code",
   "id": "49e773e8700380ce",
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2025-10-06T03:11:28.950516Z",
     "start_time": "2025-10-06T03:11:28.681290Z"
    }
   },
   "source": [
    "_ = finder.compute_jacobians(finder.fixed_points, plot=True)"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 300x200 with 1 Axes>"
      ],
      "image/png": "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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    }
   ],
   "execution_count": 13
  },
  {
   "cell_type": "markdown",
   "id": "a1a7df686a3bb68f",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "This is an unstable fixed point, because one of its eigenvalues has the real part bigger than 1."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b9e1a94399ffa6a1",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "## Further reading"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7a4f436e37606967",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "- For more details about how to perform bifurcation analysis and phase plane analysis, please see the tutorial of [Low-dimensional Analyzers](../tutorial_analysis/lowdim_analysis.ipynb).\n",
    "- A good example of phase plane analysis and bifurcation analysis is the decision-making model, please see the tutorial in [Analysis of a Decision-making Model](../tutorial_analysis/decision_making_model.ipynb)\n",
    "- If you want to how to analyze the slow points (or fixed points) of your high-dimensional dynamical models, please see the tutorial of [High-dimensional Analyzers](../tutorial_analysis/highdim_analysis.ipynb)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "BrainPy",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
